LennardJones(spatstat)
LennardJones()所属R语言包：spatstat
The Lennard-Jones Potential
Lennard-Jones势
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Creates the Lennard-Jones pairwise interaction structure which can then be fitted to point pattern data.
创建的Lennard-Jones对相互作用的结构，然后可以配点模式的数据。
用法----------Usage----------
LennardJones(sigma0=NA)
参数----------Arguments----------
参数：sigma0
Optional. Initial estimate of the parameter sigma. A positive number.
可选。初步估计参数sigma。一个正数。
Details
详细信息----------Details----------
In a pairwise interaction point process with the Lennard-Jones pair potential (Lennard-Jones, 1924) each pair of points in the point pattern, a distance d apart, contributes a factor
在对相互作用的Lennard-Jones对潜在（的Lennard-Jones，1924），每个点对点模式点的过程中，的距离d外，作出贡献的一个因素
to the probability density, where sigma and epsilon are positive parameters to be estimated.
的概率密度，sigma和epsilon是积极的待估参数。
See Examples for a plot of this expression.
示例，请参见这个表达式的图。
This potential causes very strong inhibition between points at short range, and attraction between points at medium range. The parameter sigma is called the characteristic diameter and controls the scale of interaction. The parameter epsilon is called the well depth and determines the strength of attraction. The potential switches from inhibition to attraction at d=sigma. The maximum value of the pair potential is exp(epsilon) occuring at distance d = 2^(1/6) * sigma. Interaction is usually considered to be negligible for distances d > 2.5 * sigma * max(1, epsilon^(1/6)).
这种潜在的点与点之间在短距离内，在中距离点之间的吸引力产生很强的抑制作用。参数sigma称为特征直径和控制的相互作用的规模。参数epsilon被称为井的深度和吸引力的强弱决定。的潜在开关从抑制吸引力在d=sigma。对潜在的最大值是exp(epsilon)在距离发生d = 2^(1/6) * sigma。通常被认为是可以忽略不计的距离d > 2.5 * sigma * max(1, epsilon^(1/6))互动。
This potential is used to model interactions between uncharged molecules in statistical physics.
使用这种潜力是不带电荷的分子之间的相互作用在统计物理模型。
The function ppm(), which fits point process models to point pattern data, requires an argument of class "interact" describing the interpoint interaction structure of the model to be fitted. The appropriate description of the Lennard-Jones pairwise interaction is yielded by the function LennardJones(). See the examples below.
的功能ppm()，适合点模式数据点过程模型，需要一个参数的类"interact"描述INTERPOINT互动结构的模型被安装。的Lennard-Jones对相互作用的适当的描述可以得到由该函数LennardJones()。请参见下面的例子。
值----------Value----------
An object of class "interact" describing the Lennard-Jones interpoint interaction structure.
对象的类"interact"描述的Lennard-Jones INTERPOINT互动结构。
标度----------Rescaling----------
To avoid numerical instability, the interpoint distances d are rescaled when fitting the model.
为了避免数值不稳定，INTERPOINT距离d重新调整时，拟合模型。
Distances are rescaled by dividing by sigma0. In the formula for v(d) above, the interpoint distance d will be replaced by d/sigma0.
距离重新调整除以sigma0。公式为v(d)以上，INTERPOINT距离d将取代d/sigma0。
The rescaling happens automatically by default. If the argument sigma0 is missing or NA (the default), then sigma0 is taken to be the minimum nearest-neighbour distance in the data point pattern (in the call to ppm).
默认情况下，自动重新标度发生。如果参数sigma0丢失或NA（默认值），然后sigma0是最低的最近邻距离的数据点模式（在调用<X >）。
If the argument sigma0 is given, it should be a positive number, and it should be a rough estimate of the parameter sigma.
如果参数sigma0是给定的，它应该是一个正数，它应该是一个粗略的估计的参数sigma。
The “canonical regular parameters” estimated by ppm are theta1 = 4 * epsilon * (sigma/sigma0)^12 and theta2 = 4 * epsilon * (sigma/sigma0)^6.
“规范常规参数”估计的ppm是theta1 = 4 * epsilon * (sigma/sigma0)^12和theta2 = 4 * epsilon * (sigma/sigma0)^6。
警告和错误----------Warnings and Errors----------
Fitting the Lennard-Jones model is extremely unstable, because of the strong dependence between the functions d^(-12) and d^(-6). The fitting algorithm often fails to converge. Try increasing the number of iterations of the GLM fitting algorithm, by setting gcontrol=list(maxit=1e3) in the call to ppm.
装修的Lennard-Jones模型是非常不稳定的，因为强烈的依赖关系的功能d^(-12)和d^(-6)。拟合算法往往不能收敛。尝试增加的GLM拟合算法的迭代的数目，通过设置gcontrol=list(maxit=1e3)在调用ppm。
Errors are likely to occur if this model is fitted to a point pattern dataset which does not exhibit both short-range inhibition and medium-range attraction between points. The values of the parameters sigma and epsilon may be NA (because the fitted canonical parameters have opposite sign, which usually occurs when the pattern is completely random).
错误都可能发生，如果这种模式被安装到一个点模式不表现抑制作用短程和中程吸引点之间的数据集。的参数值sigma和epsilon是NA（因为安装规范的参数有相反的符号，这通常发生时的格局完全是随机的）。
An absence of warnings does not mean that the fitted model is sensible. A negative value of epsilon may be obtained (usually when the pattern is strongly clustered); this does not correspond to a valid point process model, but the software does not issue a warning.
的警告并不意味着没有合适的模型是合理的。负值可能获得的epsilon（通常是强烈聚类模式时），这不符合一个有效的点过程模型，但该软件不会发出警告。
（作者）----------Author(s)----------
Adrian Baddeley
<a href="mailto:Adrian.Baddeley@csiro.au">Adrian.Baddeley@csiro.au</a>
<a href="http://www.maths.uwa.edu.au/~adrian/">http://www.maths.uwa.edu.au/~adrian/</a>
and Rolf Turner
<a href="mailto:r.turner@auckland.ac.nz">r.turner@auckland.ac.nz</a>
参考文献----------References----------
Proc Royal Soc London A 106, 463–477.
参见----------See Also----------
ppm, pairwise.family, ppm.object
ppm，pairwise.family，ppm.object
实例----------Examples----------
data(demopat)
demopat
X <- unmark(demopat)
X
fit <- ppm(X, ~1, LennardJones(), rbord=500)
fit
plot(fitin(fit), xlim=c(0,50))
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
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发表于 2012-9-30 13:41:56
